Given the following algorithms, find the recurrence relation $\backslash ($ T$($N$)\backslash )$ :

$```$

$1.$ function $($int n$)\{$

if $($n return;

for $($int i$=1$; i; i$++)$

function$($n$-1)$

$\}$

$```$

$```$

$2.$ int fact$($int n$)\{$

if $($n $==0)\{$ return $1$;$\}$

return n $*$ fact$($n$-1)$;

$\}$

$```$

$```$

$3.$ int fib$($int n$)\{$

if $($n return n;$\}$

return fib$($n$-1)+$ fib$($n$-2)$;

$\}$

$```$ Can you solve this using handwritten steps